In this paper, we consider equilateral lattice polygons in general planar lattices, extending Ball's theorem in some sense.
If a planar lattice contains the vertices of an equilateral triangle, then the lattice is similar to a sublattice of Z³ in R³, and it contains the vertices of a ...
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The family of lattices in the current study is based on uniform tilings by regular convex polygons and star-polygons, specifically star -, and -gons [80].
Mar 18, 2017 · A lattice point in the plane is any point that has integer coordinates. A lattice polygon is a polygon whose.
Dec 13, 2013 · If you don't require that the lattice be square then you can even have a planar equilateral "pentagon": start with an equilateral triangle of ...
In this paper we consider equilateral polygons that can be embedded in the unit lattice of ℝk. These are called lattice equilateral polygons. We show that for ...
Feb 3, 2012 · This can be done w.l.o.g. For every lattice point P:(p,q) we get an equilateral triangle with vertex P and a third vertex X (we also get another ...
Apr 16, 2022 · A lattice polygon is a polygon whose vertices have integer coordinates. 1. Find the area of each of the following lattice polygons below and on ...
An equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a ...
The simplest question concerning embeddability is this: is the equilateral triangle embeddable in Z2? That is, are there lattice points in the plane forming the ...